Distinguished tame supercuspidal representations and odd orthogonal periods
| Autor: | Jeffrey Hakim, Joshua M. Lansky |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Pure mathematics Induced representation 010102 general mathematics 16. Peace & justice 01 natural sciences Mathematics (miscellaneous) General theory 0103 physical sciences Orthogonal group 010307 mathematical physics 0101 mathematics Representation theory of the Poincaré group Local field Representation theory of finite groups Mathematics |
| Zdroj: | Representation Theory of the American Mathematical Society. 16:276-316 |
| ISSN: | 1088-4165 |
| DOI: | 10.1090/s1088-4165-2012-00418-6 |
| Popis: | We further develop and simplify the general theory of distinguished tame supercuspidal representations of reductive p p -adic groups due to Hakim and Murnaghan, as well as the analogous theory for finite reductive groups due to Lusztig. We apply our results to study the representations of G L n ( F ) \mathrm {GL}_n(F) , with n n odd and F F a nonarchimedean local field, that are distinguished with respect to an orthogonal group in n n variables. In particular, we determine precisely when a supercuspidal representation is distinguished with respect to an orthogonal group and, if so, that the space of distinguishing linear forms has dimension one. |
| Databáze: | OpenAIRE |
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